Method for rapid calculation of tear film lipid and aqueous layer thickness and ocular surface refractive index from interferometry spectra

ABSTRACT

A method for determining optical properties of a corneal region. The method includes the steps of obtaining a combined tear film aqueous layer plus lipid layer thickness; obtaining a tear film lipid layer thickness; subtracting the tear film lipid layer thickness from the combined tear film aqueous layer plus lipid layer thickness to obtain a tear film aqueous layer thickness; and determining a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent application Ser. No. 14/298,036, filed Jun. 6, 2014, which is incorporated herein by reference in its entirety. The present application is also related to U.S. patent application Ser. No. 14/298,176 (published as U.S. Publication No. US 2015-0351627 A1) to Huth and Tran, “Fast Absolute-Reflectance Method for the Determination of Tear Film Lipid Layer Thickness,” filed Jun. 6, 2014, which is incorporated herein by reference in its entirety.

BACKGROUND

The present invention relates to methods for rapid calculation of tear film lipid and aqueous layer thickness and ocular surface refractive index from interferometry spectra.

While a method exists for calculation of parameters such as tear film lipid and aqueous layer thicknesses and ocular surface refractive index using interferometry spectra, this method is relatively slow, requiring many minutes to perform calculations using existing computing platforms. What is needed are improved methods which reduce calculation times using existing computing platforms.

SUMMARY

In one embodiment, the invention provides a method for determining optical properties of a corneal region. The method includes the steps of obtaining a combined tear film aqueous layer plus lipid layer thickness; obtaining a tear film lipid layer thickness; subtracting the tear film lipid layer thickness from the combined tear film aqueous layer plus lipid layer thickness to obtain a tear film aqueous layer thickness; and determining a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness.

In another embodiment the invention provides a system for determining optical properties of a corneal region. The system includes a wavelength-dependent optical interferometer and a controller. The controller is in communication with the interferometer and is configured to obtain a combined tear film aqueous layer plus lipid layer thickness, obtain a tear film lipid layer thickness, subtract the tear film lipid layer thickness from the combined tear film aqueous layer plus lipid layer thickness to obtain a tear film aqueous layer thickness, and determine a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness.

Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows the results of the fitting procedure after using an initial thickness estimate of 3000 nm for the combined ‘aqueous+lipid’ layer thickness.

FIG. 2 shows results of a curve-fitting procedure using the presently-disclosed methods.

FIG. 3 shows results of a curve-fitting procedure with the same data as in FIG. 2 using the methods of the 557 patent.

FIG. 4 shows results of a curve-fitting procedure using the presently-disclosed methods.

FIG. 5 shows results of a curve-fitting procedure with the same data as in FIG. 4 using the methods of the '557 patent.

FIG. 6 shows results of a curve-fitting procedure using the presently-disclosed methods.

FIG. 7 shows results of a curve-fitting procedure with the same data as in FIG. 6 using the methods of the '557 patent.

FIG. 8 shows results of a curve-fitting procedure using the presently-disclosed methods.

FIG. 9 shows results of a curve-fitting procedure with the same data as in FIG. 8 using the methods of the '557 patent.

FIG. 10 shows results of a curve-fitting procedure using the presently-disclosed methods.

FIG. 11 shows results of a curve-fitting procedure with the same data as in FIG. 10 using the methods of the '557 patent.

FIG. 12 shows the correlation between the tear film lipid layer thickness values obtained using the tear film lipid layer thickness values using the methods from co-pending application Ser. No. 14/298,176 and those obtained using the presently-disclosed methods for the data from Examples 1-3.

FIG. 13 shows the correlation between the tear film aqueous layer thickness values obtained using the methods of the '293 patent with the methods from co-pending application Ser. No. 14/298,176 and those obtained using the present methods for the data from Examples 1-3.

FIG. 14 shows the results of a curve-fitting procedure using a second-order exponential c-term.

FIGS. 15 and 16 show spectra curve-fitted using a second-order (FIG. 15) or first-order (FIG. 16) exponential c-term.

FIG. 17 shows the correlation between tear film lipid layer thickness values obtained using the methods of the tear film lipid layer thickness values using the methods from co-pending application Ser. No. 14/298,176 and those obtained using the present methods for spectra from Example 4, with the exception of spectrum sub12#93.

FIG. 18 shows the correlation between tear film aqueous layer thickness values obtained using the methods of the '293 patent with the methods from co-pending application Ser. No. 14/298,176 and those obtained using the present methods for spectra from Example 4.

DETAILED DESCRIPTION

Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways.

The methods disclosed herein offer a significant improvement over existing techniques, including those of the recently-issued patent method (Huth et al., U.S. Pat. No. 8,602,557, referred to herein as the '557 patent; incorporated herein by reference in its entirety). The '557 method takes as long as 475 seconds to complete all calculations for a single interferometry spectrum. This new method requires no more than a few seconds for the calculations, and thus considerably shortens calculation time and also allows one to utilize more interferometry spectra for data analysis, a critical need to provide more statistically robust data and to account for the effects of eye blink dynamics on these tear film parameters. This new method completes all calculations and provides identical results to the method of the '557 patent for lipid and aqueous layer thickness, surface refractive index, fitting error and b and c-terms in seconds (e.g., 10.9 sec. vs. 475 sec.; 3.6 sec. vs. 400 sec.; and 11.8 sec. vs. 408 sec.).

The new methods combine an existing method for ‘aqueous+lipid’ thickness (Huth et al. U.S. Pat. No. 7,959,293, referred to herein as the '293 patent, incorporated herein by reference in its entirety) with the co-pending method for fast lipid thickness (U.S. patent application Ser. No. 14/298,176), along with the methods in U.S. Pat. No. 8,602,557 for all measurements including lipid and aqueous layer thickness, surface refractive index, fitting error, and b and c-terms. The procedures of the '557 patent are modified by using ‘aqueous+lipid’ and lipid thickness inputs from the aforementioned fast methods, wherein the lipid thickness value is subtracted from the ‘aqueous+lipid’ thickness value to obtain an aqueous-only thickness value. As a result, the current calculation matrix of the '557 patent is reduced from a 6×7 matrix (6 aqueous layer thickness starting values and 7 lipid layer thickness starting values for the fitting algorithm) to a single matrix-fitting calculation, thereby reducing the time required for completing all calculations by a factor of approximately 1/(6×7)=1/42.

EXAMPLE 1

The first step in the method of the present invention uses the methods in Huth et al. U.S. Pat. No. 7,959,293, wherein interferometry spectra are produced and relative reflectance data are collected for a series of wavelengths, and wherein v2=relative reflectance and wherein v1=wavelength in nm, and the v1 and v2 data are fit to the following function using a Statistica (StatSoft®, Tulsa, Okla.) software program (Version 7.1, Series 1006b): v2=−a−b*v1−c*v1**2+d*(1+(e/2*d)*cos((16.745*g/v1)+h))*Exp(−J/v1**2)

The Non-linear Estimation method within the Statistica software is used, wherein the equation for v2 above is input as the function to be estimated into the space provided in the user specified regression, least squares module. The Statistica software program uses the Levenburg-Marquardt algorithm to achieve a minimum in the sum of squares of the differences between the interferometer-measured spectrum and a fitted spectrum, fit to the function above, wherein the variables a, b, c, d, e, g, h, and J are iteratively changed. Other mathematical algorithms for fitting data are available within Statistica and other software platforms and can also be employed. This software module requires the number of calculation/fitting iterations to be selected. In one embodiment, 50-300 iterations were found to be acceptable, although in various other embodiments other lower or higher numbers of iterations are also acceptable and can be easily determined by an evaluation of the fit. The program also requires starting values for the variable terms, i.e. a, b, c, d, e, g, h, and J, where the g-term is the initial estimate of the tear film ‘aqueous+lipid’ layer thickness.

The spectrum in this example was taken from a human subject who was not wearing contact lenses, with the identification number sub21#43. FIG. 1 shows the results of the fitting procedure after using an initial thickness estimate of 3000 nm for the combined ‘aqueous+lipid’ layer thickness. A result of 2942.7 nm total thickness for the combined ‘aqueous+lipid’ layer thickness was obtained.

The next step in the method is to calculate the tear film lipid layer thickness. This is calculated using the methods described in co-pending application 14/298,176, using input values for the a-term of 65 nm and for the b-term of 0.66, and the following equation: v6=((1−((8*v1*v2**2*v3)/((v1**2+v2**2)*(V2**2+v3**2)+4*v1*v2**2*v3+((v1**2−v2**2)*(v2**2−v3**2)*(cos(4*3.14159*v2*a*0.98666/v4)))))))*b/v5

where the input data are v6=R(λ) meas tear lipid sample (measured % relative reflectance) and wherein v1=n₀ air=1, v2=n₁(λ) tear film lipid (Sellmeier-form), v3=n₂ (λ) aqueous, v4=measured λ and v5=R(λ) absolute BK7 reference (BK7 absolute R calc)/100 and wherein a Levenberg-Marquardt algorithm is used for fitting the data. The results obtained are shown in Table 1.

TABLE 1 Level of confidence: 95.0% (alpha = 0.050) Estimate Standard t-value p-level Lo. Conf Up. Conf a 31.77767 0.130980 242.6155 0.00 31.52055 32.03480 b  0.37007 0.000584 633.6999 0.00  0.36892  0.37122 a 31.77767 0.130980 242.6155 0.00 31.52055 32.03480 b  0.37007 0.000584 633.6999 0.00  0.36892  0.37122

The value obtained for the a-term, the tear film lipid layer thickness, is 31.78 nm. The calculation of the tear film lipid layer thickness can also be completed in a parallel computer-processing step along with the calculation of the combined ‘aqueous+lipid’ layer thickness.

Taking the thickness value for the combined ‘aqueous+lipid’ layer thickness of 2942.7 nm from the first step, the tear film lipid layer-only thickness of 31.78 nm is subtracted and the aqueous-only thickness of 2910.92 nm is obtained. These values for aqueous layer-only thickness and lipid layer-only thickness are input as starting values into the following modified Matlab software program (MATLAB R2013a), taken from U.S. Pat. No. 8,602,557, incorporated herein in its entirety by reference, and modified where indicated.

% Program for eye reflectance - Statistica inputs (no variable aqueous or lipid layer thicknesses) for one spectrum % % Remarks: b_parameter starting value:1, epithelium refractive index starting value:1.338+0.00306.*(1000./L).{circumflex over ( )}2 %-------------------------------------------------------------------------------------- -----------------------------------% % Aqueous layer thickness from Statistica At=2910.92% Excel read excl=xlsread(‘sub21#43.xls’); % ----------------j1_25min_-------------------------------------------------------- ---------------------------------------------% % Parameters At=At; (′557 program line: At=At−50) z2=0; % Plot of exp. data plot(excl(:,1),excl(:,2)) L=[excl(:,1)]; R=[excl(:,2)]; hold on % Loops for y=0 (′557 program line: y = 0:20:100) z2=z2+1; z=0; % Input lipid thickness from Statistica (no semi-colon or punctuation at % end) for p=31.78 (′557 program line: p = 20:20:140)

The remaining program code is identical to that in U.S. Pat. No. 8,602,557.

The following results were obtained in 7.8 seconds with an IBM ThinkPad computer with an Intel® Core™ 2 Duo CPU, T9400@2.53 GHz (1.59 GHz, 1.98 GB of RAM):

Lipid layer thickness: 35.1 nm

Aqueous layer thickness: 2969.5 nm

Corneal surface refractive index: 1.3360

b-term: 0.3760

c-term: 0.0560

error: 2.96e−6

FIG. 2 shows the fit of the results (smooth line) to the original spectrum (jagged line), based on data from subject sub21#43. The parameter results were identical to those obtained with the program code in U.S. Pat. No. 8,602,557, which took 131 seconds to run on the same computer with the same data set (i.e. from subject sub21#43). The fit obtained in FIG. 2 with the method of the present invention is substantially the same as that obtained with the method in U.S. Pat. No. 8,602,557 (FIG. 3).

EXAMPLE 2

The method of Example 1 was followed with analysis of an interferometry spectrum taken from a human subject, identification number RH1f8hr#20, wearing Acuvue 2® soft contact lenses.

The Statistica results were 1572.15 nm for the combined tear film ‘aqueous+lipid’ layer thickness and 31.53 nm for the tear film lipid layer thickness, giving 1540.60 nm for the tear film aqueous layer thickness. As with Example 1, in the present Example 2 the tear film aqueous and lipid layer thickness values were input as starting values into the revised Matlab software program. The substrate surface underlying the tear film in this case was the contact lens surface, rather than the corneal epithelium as in Example 1. Thus, the surface refractive index starting value for the Matlab software program was the published value for the bulk contact lens, 1.4055. It was determined, however, that using refractive index starting values of 1.338, 1.37, 1.4055, and 1.42 all gave identical results. Thus, the nominal refractive index starting value for the corneal epithelium, 1.338, can also be used for tear film spectra from contact lens wearers. Table 2 lists the following results, which were obtained in 3.1 seconds with the method of the present invention, compared to 467 seconds with the method in the '557 patent.

TABLE 2 Parameter present invention ′557 method Lipid layer thickness, nm 56.5 63.5 Aqueous layer thickness, nm 1507.6 1502.0 Lens surface refractive index 1.3649 1.3663 b-term 0.0297 0.0268 c-term 0.3940 0.3858 Error 1.02E−07 9.81E−08 Calculation time, seconds 3 467 Lipid layer thickness, nm 56.5 63.5 Aqueous layer thickness, nm 1507.6 1502.0 Lens surface refractive index 1.3649 1.3663 b-term 0.0297 0.0268 c-term 0.3940 0.3858 Error 1.02E−07 9.81E−08 Calculation time, seconds 3 467

The results above and fit obtained in FIG. 4 with the method of the present invention are very close to that obtained with the slower methods of U.S. Pat. No. 8,602,557 (FIG. 5) using the same data set (both of FIGS. 4 and 5 use data from subject RH1f8hr#20).

EXAMPLE 3

The method of Example 1 was followed with interferometry spectra taken from six additional subjects, none of whom was wearing contact lenses. Results are shown in Table 3. Interferometry spectra from four subjects, with identification numbers sub1#29, sub4#5, sub6#7, and sub6base#84 produced the same results for the method of the present invention as with the methods of the '557 patent. Calculation times for all four spectra were much shorter with the method of the present invention, ranging from 2.2-11.8 sec, compared to 137-408 sec for the methods of the '557 patent. Note in Table 3 that the methods of the '557 patent consistently produced longer calculation times than the method of the present invention, although different times on occasion when the calculations were repeated. It was noted that the program tended to run faster after the first calculation for the particular day.

FIGS. 6 and 7 show analyses of data for subject sub4#5 using the methods of the present invention and of the '557 patent, respectively. The fits and results are essentially identical, but the calculation times are 3.8 vs. 235 seconds, respectively. The remaining three subjects and four spectra, with identification numbers sub2DE, sub3#15, sub3#56, and sub12#93, produced close results for the method of the present invention compared to the methods of the '557 patent.

FIGS. 8 and 9 show spectrum sub2DE analyses with the method of the present invention and the methods of the '557 patent, respectively. The very low tear film aqueous layer reflectance interference oscillation amplitude in this spectrum makes the analysis challenging, which required 400 seconds with the methods of the '557 patent, whereas the present methods achieved a fit in only 3.8 seconds.

FIGS. 10 and 11 show spectrum sub3#56 analyses with the method of the present invention and the methods of the '557 patent, respectively. Table 3 shows that the original tear film lipid layer thicknesses derived from the Statistica program, which are used as input values for the present Matlab software program, are close, but different from the resulting Matlab program calculated thicknesses derived from the spectrum fits. Table 3 also shows that the present method produced closer lipid layer thickness values to those obtained from the Statistica program in those cases in which results between the methods of the '557 patent and the present methods differ.

FIG. 12 shows the correlation between the tear film lipid layer thickness values obtained using the tear film lipid layer thickness values using the methods from co-pending application Ser. No. 14/298,176 and those obtained using the presently-disclosed Matlab method lipid layer thickness values for spectra from Examples 1-3. A reasonably good correlation was found (slope=0.9961, intercept 13.267 nm and r^2=0.9051) given the nanometer measurement scale for the clinical interferometer and associated mathematics and software. The average difference found was 13 nm, which is considered good. Differences are expected due to the more rigorous calculations required for the Matlab software program, which calculates tear film aqueous and lipid layer thicknesses and either corneal surface or contact lens surface refractive indices. It can be seen from Table 3 that the differences become small as the tear film aqueous layer thickness increases, likely due to the better spectrum fits which can be obtained with additional aqueous layer thickness reflectance interference oscillations.

FIG. 13 shows the correlation between the tear film aqueous layer thickness values obtained using the methods of the '293 patent with the methods from co-pending application Ser. No. 14/298,176 and those obtained using the present Matlab method aqueous layer thickness values for spectra from Examples 1-3. A very good correlation was found (slope=0.9998, intercept 8.8298 nm and r^2=0.9981).

TABLE 3 Spectrum Stat aq/lip inputs/match Calc. time, sec Stat aq nm Stat lip nm Stat ap + lip Stat b sub1#29 3453.51/24.19/same 11.8 3453.51 24.19 3477.70 0.8265 sub4#5 1956.79/24.83/same 3.8 1956.79 24.83 1981.62 0.6836 sub6#7 3845.97/67.07/same 2.2 3845.97 67.07 3913.04 0.6762 sub6base#84 3204/80/same 2.4 3204.24 80.32 3284.56 0.2876 sub2DE original ′557 method 400 sub2DE 2542.95/79.67/close values 3.0 2542.95 79.67 2622.62 1.0323 sub3#15 original ′557 method 206 sub3#15 1555.7/41.84/close values 2.0 1555.70 41.84 1597.54 1.0761 sub3#56 original ′557 method 361 sub3#56 1386.26/42.00/close values 2.8 1386.26 42.00 1428.26 1.2879 sub12#93 orignial ′557 method 475 sub12#93 4092.98/30.66/close values 21.9 4092.98 30.66 4123.64 1.2512 Mlab lip nm Mlab b Mlab c Mlab aq nm Mlab nd Mlab error 567 Mlab calc time, sec  34.7 0.9223 0.1958 3405.6 1.3328 8.17E−06 408; 402  37.0 0.7530 0.1850 1991.4 1.3382 2.40E−05 235  71.3 0.6526 0.0204 3870.1 1.1351 1.53E−05 137  93.5 0.2227 −0.1119 3217.2 1.3369 1.83E−05 220; 156 108.6 0.6040 −0.2663 2595.4 1.1348 2.11E−05 400  95.6 0.8629 −0.0593 2457.3 1.3313 2.32E−05  71.3 1.0142 0.2230 1546.4 1.3368 2.67E−05 206  64.4 1.1702 0.2650 1553.0 1.3366 2.89E−05  64.5 1.2768 0.2084 1365.9 1.3225 1.87E−05 361  58.1 1.4258 0.2269 1371.7 1.3296 1.87E−05  39.4 1.3000 0.1199 3883.3 1.3298 1.62E−05 475  38.3 1.3487 0.1345 4053.0 1.3341 1.69E−05 Spectrum Stat aq/lip inputs/match Calc. time, sec Stat aq nm Stat lip nm Stat aq + lip Stat b sub1#29 3453.51/24.19/same 11.8 3453.51 24.19 3477.70 0.8265 sub4#5 1956.79/24.83/same 3.8 1956.79 24.83 1981.62 0.6836 sub6#7 3845.97/67.07/same 2.2 3845.97 67.07 3913.04 0.6762 sub6base#84 3204/80/same 2.4 3204.24 80.32 3284.56 0.2876 sub2DE original ′557 method 400 sub2DE 2542.95/79.67/close values 3.0 2542.95 79.67 2622.62 1.0323 sub3#15 original ′557 method 206 sub3#15 1555.7/41.84/close values 2.0 1555.70 41.84 1597.54 1.0761 sub3#56 original ′557 method 361 sub3#56 1386.26/42.00/close values 2.8 1386.26 42.00 1428.26 1.2879 sub12#93 original ′557 method 475 sub12#93 4092.98/30.66/close values 21.9 4092.98 30.66 4123.64 1.2512 Mlab lip nm Mlab b Mlab c Mlab aq nm Mlab nd Mlab error 567 Mlab calc time, sec  34.7 0.9223 0.1958 3405.6 1.3328 8.17E−06 408; 402  37.0 0.7530 0.1850 1991.4 1.3382 2.40E−05 235  71.3 0.6526 0.0204 3870.1 1.3351 1.53E−05 137  93.5 0.2227 −0.1119 3217.2 1.3369 1.83E−05 220; 156 108.6 0.6040 −0.2663 2595.4 1.3348 2.11E−05 400  95.6 0.8629 −0.0593 2457.3 1.3313 2.32E−05  71.3 1.0142 0.2230 1546.4 1.3368 2.67E−05 206  64.4 1.1702 0.2650 1553.0 1.3366 2.89E−05  64.5 1.2768 0.2084 1365.9 1.3295 1.87E−05 361  58.1 1.4258 0.2269 1371.7 1.3296 1.87E−05  39.4 1.3000 0.1199 3883.3 1.3298 1.62E−05 475  38.3 1.3487 0.1345 4053.0 1.3341 1.69E−05

EXAMPLE 4

In one embodiment, the method of Example 1 was followed using the same interferometry spectra as shown in Table 3. A faster computer was used for the spectrum fits in this example, an Intel® Core™ i5-4300U CPU@1.90, 2.50 GHz with 4.00 GB RAM and a 64-bit operating system. In this embodiment the exponential term for the c-term multiplier of the Matlab program was changed from a first-order exponential to a second-order exponential (results shown in Table 4):

From * exp(−b(5).*(1000./L).^1.0)) in the new program herein for the mathematical function to *exp(−b(5).*(1000./L).^2.0)) (Note that this change is made on three program lines).

TABLE 4 Spectrum Stat aq/lip inputs/match Calc. time, sec Stat aq nm Stat lip nm Stat aq + lip Stat b RHIf8hr#20 1540.6/31.53/close values 2.4 1540.62 31.53 1572.15 0.0238 sub3#15 1555.7/41.84/close values 2.5 1555.70 41.84 1597.54 1.0761 sub2DE 2542.95/79.67/close values 3.1 2542.95 79.67 2622.62 1.0323 sub3#56 1386.26/42.00/close values 1.8 1386.26 42.00 1428.26 1.2879 sub6base#84 3204/80/close values 1.9 3204.24 80.32 3284.56 0.2876 sub4#5 1956.79/24.83/close values 3.5 1956.79 24.83 1981.62 0.6836 sub1#29 3453.51/24.19/close values 3.7 3453.51 24.19 3477.70 0.8265 sub21#43 2910.92/31.78/same 7.8 2910.92 31.78 2942.70 0.3701 sub6#7 3845.97/67.07/same 2.2 3845.97 67.07 3913.04 0.6762 sub12#93* 4092.98/30.66/close values 3.2 4092.98 30.66 4123.64 1.2512 sub12#93** 4092.98/30.66/close values 3.4 4092.98 30.66 4123.64 1.2512 Mlab lip nm Mlab b Mlab c Mlab aq nm Mlab nd Mlab error 47.0 0.0241 0.1146 1518.2 1.3630 1.09E−07 56.3 1.0413 0.0823 1561.9 1.3364 2.90E−05 99.4 0.8619 −0.0336 2601.2 1.3348 2.11E−05 50.8 1.2829 0.0633 1379.9 1.3298 1.88E−05 84.2 0.2844 0.0059 3222.2 1.3367 1.91E−05 17.8 0.6834 −0.0288 2014.1 1.3377 2.74E−05 14.5 0.8188 −0.0301 3429.6 1.3329 9.20E−06 16.1 0.3684 −0.0773 2990.3 1.3357 2.88E−06 62.2 0.7345 0.0196 3874.9 1.3350 1.61E−05 19.3 1.2421 −0.058 6131.5 1.3316 4.00E−06 38.4 1.3505 0.1369 3879.5 1.3298 1.61E−05 Spectrum Stat aq/lip inputs/match Calc. time, sec Stat aq nm Stat lip nm Stat aq + lip Stat b RHIf8hr#20 1540.6/31.53/close values 2.4 1540.62 31.53 1572.15 0.0238 sub3#15 1555.7/41.84/close values 2.5 1555.70 41.84 1597.54 1.0761 sub2DE 2542.95/79.67/close values 3.1 2542.95 79.67 2622.62 1.0323 sub3#56 1386.26/42.00/close values 1.8 1386.26 42.00 1428.26 1.2879 sub6base#84 3204/80/close values 1.9 3204.24 80.32 3284.56 0.2876 sub4#5 1956.79/24.83/close values 3.5 1956.79 24.83 1981.62 0.6836 sub1#29 3453.51/24.19/close values 3.7 3453.51 24.19 3477.70 0.8265 sub21#43 2910.92/31.78/same 7.8 2910.92 31.78 2942.70 0.3701 sub6#7 3845.97/67.07/same 2.2 3845.97 67.07 3913.04 0.6762 sub12#93* 4092.98/30.66/close values 3.2 4092.98 30.66 4123.64 1.2512 sub12#93** 4092.98/30.66/close values 3.4 4092.98 30.66 4123.64 1.2512 Mlab lip nm Mlab b Mlab c Mlab aq nm Mlab nd Mlab error 47.0 0.0241 0.1146 1518.2 1.3630 1.09E−07 56.3 1.0413 0.0823 1561.9 1.3364 2.90E−05 99.4 0.8619 −0.0336 2601.2 1.3348 2.11E−05 50.8 1.2829 0.0633 1379.9 1.3298 1.88E−05 84.2 0.2844 0.005 3222.2 1.3367 1.91E−05 17.8 0.6834 −0.0288 2014.1 1.3377 2.74E−05 14.5 0.8188 −0.0301 3429.6 1.3329 9.20E−06 16.1 0.3684 −0.0773 2990.3 1.3357 2.88E−06 62.2 0.7345 0.0196 3874.9 1.3350 1.61E−05 19.3 1.2421 −0.058 6131.5 1.3316 4.00E−06 38.4 1.3505 0.1369 3879.5 1.3298 1.61E−05 *poor fit; **good fit with exp{circumflex over ( )}1 for c-term

It can be seen in Table 4 that, with the exception of a single spectrum, sub12#93, values close to those obtained in Table 3 were produced. FIG. 14 shows the results of the fit obtained for spectrum RHlf8hr#20 as an example for the usage of the second-order exponential c-term.

The present method Matlab program with a second-order exponential for the c-term achieved good fits for all other spectra in Table 4 (data not shown), with the exception of spectrum sub12#93. This is seen in comparing FIG. 15, showing the second order exponential c-term result, with FIG. 16, showing the first-order exponential c-term result. Thus, the second-order exponential c-term can be used as well as the first-order exponential c-term, with some exceptions.

FIG. 17 shows the correlation between tear film lipid layer thickness values obtained using the methods of the tear film lipid layer thickness values using the methods from co-pending application Ser. No. 14/298,176 and those obtained using the present Matlab method lipid layer thickness values for spectra from Example 4, with the exception of spectrum sub12#93. A reasonably good correlation was again found (slope=1.2268, intercept 7.8782 nm and r^2=0.8536) given the nanometer measurement scale for the clinical interferometer and associated mathematics and software. The average difference found for the data set was 2.8 nm, as some Statistica values were higher and some were lower than the Matlab-fitted values for the same spectra.

FIG. 18 shows the correlation between tear film aqueous layer thickness values obtained using the methods of the '293 patent with the methods from co-pending application Ser. No. 14/298,176 and those obtained using the present Matlab method aqueous layer thickness values for spectra from Example 4. A very good correlation was found (slope=1.0086, intercept 0.3617 nm and r^2=0.9985).

The method of the present invention also includes methods wherein only one of the tear film aqueous or lipid layer thickness values derived from the Statistica program are used as input starting values, and the Matlab software is allowed to run the other 7× matrix calculations for lipid layer thickness (when aqueous thickness is input) or the 6× matrix calculations for aqueous layer thickness (when lipid thickness is input). Both of these alternative methods result in significantly improved shorter Matlab software program calculation times due to the reduced sizes of the calculation matrices.

In various embodiments, the disclosed methods may be carried out on a computing system in communication with an interferometer (e.g. a wavelength-dependent interferometer). The computing system may include one or more computer systems in communication with one another through various wired and wireless communication means which may include communications through the Internet and/or a local network (LAN). Each computer system may include an input device, an output device, a storage medium (including non-transient computer-readable media), and a processor such as a microprocessor. Possible input devices include a keyboard, a computer mouse, a touch screen, and the like. Output devices include a cathode-ray tube (CRT) computer monitor, a LCD or LED computer monitor, and the like. Storage media may include various types of memory such as a hard disk, RAM, flash memory, and other magnetic, optical, physical, or electronic memory devices. The processor may be any suitable computer processor for performing calculations and directing other functions for performing input, output, calculation, and display of data in the disclosed system. Implementation of the computing system may include generating a set of instructions and data that are stored on one or more of the storage media and operated on by a controller. Thus, one or more controllers may be programmed to carry out embodiments of the disclosed invention. The data associated with the system may include image data, numerical data, or other types of data.

Various features and advantages of the invention are set forth in the following claims. 

What is claimed is:
 1. A method for determining optical properties of a corneal region, comprising the steps of: obtaining a combined tear film aqueous layer plus lipid layer thickness; obtaining a tear film lipid layer thickness; subtracting the tear film lipid layer thickness from the combined tear film aqueous layer plus lipid layer thickness to obtain a tear film aqueous layer thickness; and determining a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness, wherein at least one of obtaining a combined tear film aqueous layer plus lipid layer thickness and obtaining a tear film lipid layer thickness comprises measuring a tear film aqueous layer plus lipid layer relative reflectance spectrum using a wavelength-dependent optical interferometer.
 2. The method of claim 1, wherein obtaining a tear film lipid layer thickness comprises measuring a tear film aqueous layer plus lipid layer relative reflectance spectrum using a wavelength-dependent optical interferometer, and converting the measured tear film aqueous plus lipid layer relative reflectance spectrum to a calculated absolute reflectance spectrum.
 3. The method of claim 2, wherein obtaining a tear film lipid layer thickness further comprises determining a tear film lipid layer thickness using an iterative curve fitting procedure.
 4. The method of claim 2, wherein determining a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness comprises a matrix fitting calculation based on the tear film lipid layer thickness and the tear film aqueous layer thickness.
 5. The method of claim 4, wherein each of the lipid layer thickness and the aqueous layer thickness comprises an initial estimate and wherein the matrix fitting calculation determines a final lipid layer thickness and a final aqueous layer thickness.
 6. The method of claim 5, wherein the matrix fitting calculation comprises finding a best fit curve for an observed a tear film reflectance spectrum obtained using a wavelength-dependent optical interferometer.
 7. The method of claim 4, wherein the matrix fitting calculation comprises fitting the calculated absolute reflectance spectrum to a mathematical construct based upon a characteristic mathematical matrix of a plurality of thin film layers comprising in sequence, from top to bottom: air as a boundary, a tear film lipid layer, a tear film aqueous layer, and a corneal tissue as a semi-infinite substrate.
 8. The method of claim 7, wherein the corneal tissue comprises an epithelium.
 9. A system for determining optical properties of a corneal region, comprising: a wavelength-dependent optical interferometer; and a controller in communication with the interferometer, the controller configured to obtain a combined tear film aqueous layer plus lipid layer thickness, obtain a tear film lipid layer thickness, subtract the tear film lipid layer thickness from the combined tear film aqueous layer plus lipid layer thickness to obtain a tear film aqueous layer thickness, and determine a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness, wherein the controller, in order to at least one of obtain a combined tear film aqueous layer plus lipid layer thickness and obtain a tear film lipid layer thickness, is further configured to measure a tear film aqueous layer plus lipid layer relative reflectance spectrum using the wavelength-dependent optical interferometer.
 10. The system of claim 9, wherein the controller, in order to obtain a tear film lipid layer thickness, is further configured to measure a tear film aqueous layer plus lipid layer relative reflectance spectrum using the wavelength-dependent optical interferometer, and convert the measured tear film aqueous plus lipid layer relative reflectance spectrum to a calculated absolute reflectance spectrum.
 11. The system of claim 10, wherein the controller, in order to obtain a tear film lipid layer thickness, is further configured to determine a tear film lipid layer thickness using an iterative curve fitting procedure.
 12. The system of claim 10, wherein the controller, in order to determine a corneal layer refractive index based on the tear film lipid layer thickness and the tear film aqueous layer thickness, is further configured to perform a matrix fitting calculation based on the tear film lipid layer thickness and the tear film aqueous layer thickness.
 13. The system of claim 12, wherein each of the lipid layer thickness and the aqueous layer thickness comprises an initial estimate and wherein the matrix fitting calculation determines a final lipid layer thickness and a final aqueous layer thickness.
 14. The system of claim 12, wherein the controller, to perform the matrix fitting calculation, is further configured to fit the calculated absolute reflectance spectrum to a mathematical construct based upon a characteristic mathematical matrix of a plurality of thin film layers comprising in sequence, from top to bottom: air as a boundary, a tear film lipid layer, a tear film aqueous layer, and a corneal tissue as a semi-infinite substrate.
 15. The system of claim 14, wherein the corneal tissue comprises an epithelium.
 16. The system of claim 15, wherein the controller, to perform the matrix fitting calculation, is further configured to find a best fit curve for an observed a tear film reflectance spectrum obtained using the wavelength-dependent optical interferometer. 